Existence results of a nonlocal superlinear problems Involving $p(x)-$Laplacian near to zero
Resumo
In this work, by using a variational approach, we give a result on the existence and multiplicity of solutions concerned a class of nonlocal elliptic problems with variable exponent.
Downloads
Referências
M. Allaoui, A. El Amrouss, A. Ourraoui, Existence results for a class of nonlocal problems involving p(x)−Laplacian, Math. Meth. Appl. Sci. 2016, 39 824-832. https://doi.org/10.1002/mma.3524
C. O. Alves, F. J. S. A. Correa, G. M. Figueiredo, On a class of nonlocal elliptic problems with critical growth, DEA 2 (2010) 409-417. https://doi.org/10.7153/dea-02-25
C. O. Alves, F. J. S. A. Correa, On existence of solutions for a class of problem involving a nonlinear operator, Comm. Appl. Nonlinear Anal. 8 (2001) 43-56.
G. Autuori, P. Pucci, M. C. Salvatori, Asymptotic stability for anisotropic Kirchhoff systems, J. Math. Anal. Appl. 352 (2009) 149-165. https://doi.org/10.1016/j.jmaa.2008.04.066
M. Avci, B. Cekic and R. A. Mashiyev, Existence and multiplicity of the solutions of the p(x)−Kirchhoff type equation via genus theory, Math. Methods Appl. Sci. 34 (14), 1751-1759. https://doi.org/10.1002/mma.1485
K. Ben Ali, A. Ghanmi, and K. Kefi, Minimax method involving singular p(x)−Kirchhoff equation, Journal of Mathematical Physics, Volume 58, Issue 11 https://doi.org/10.1063/1.5010798
M. Chipot and B. Lovat, Some remarks on nonlocal elliptic and parabolic problems, Nonlinear Anal., 30 (7) (1997), 4619-4627. https://doi.org/10.1016/S0362-546X(97)00169-7
G. Dai, Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)−Laplacian, App. Anal. (2011) 1-20.
DE. Edmunds, J. Rakosnık. Sobolev embedding with variable exponent. Studia Math. 2000; 143: 267-293. https://doi.org/10.4064/sm-143-3-267-293
X. L. Fan, D. Zhao, A class of De Giorgi type and Holder continuity, Nonlinear Anal. 36 (1999) 295-318. https://doi.org/10.1016/S0362-546X(97)00628-7
X. L. Fan, Global C1,α regularity for variable exponent elliptic equations in divergence form, J. Differential Equations 235 (2) (2007) 397-417.
X. L. Fan, On nonlocal p(x)−Laplacian Dirichlet problems, Nonlinear Anal. 72 (2010) 3314-3323. 13. X.L. Fan, D.Zhao, On the spaces Lp(x) (Ω) and W m,p(x) (Ω), J.Math.Anal.Appl, 263(2001)424-446. https://doi.org/10.1016/j.na.2009.12.012
M. G. Figueiredo, Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument, J. Math. Anal. Appl. 401 (2013) 706-713. https://doi.org/10.1016/j.jmaa.2012.12.053
H. P. Heinz, Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems, J. Differential Equations 66 (2) (1987) 263-300. https://doi.org/10.1016/0022-0396(87)90035-0
G. Kirchhok, Vorlesungen uber mathematische Physik : Mechanik, Leipzig : B.G. Teubner, 1883.
G. M Bisci, V. Radulescu, R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia of Mathematics and its Applications, vol. 162, Cambridge University Press, Cambridge, 2016.
A. Ourraoui, On an elliptic equation of p−Kirchhoff type with convection term, C.R.Acad.Sci.Paris, Ser.I 354(2016)253-256. https://doi.org/10.1016/j.crma.2015.10.025
A. Ourraoui, On Nonlocal p(x)-Laplacian problems involving No Flux boundary condition, Note Mat. 35 (2015) no. 2, 69-81.
A. Ourraoui, Multiplicity results for Steklov problem with variable exponent, Applied Mathematics and Computation 277:(2016) 34-43. https://doi.org/10.1016/j.amc.2015.12.043
M. Ruzicka , Flow of shear dependent electrorheological fluids, CR Math. Acad. Sci. Paris 329 (1999) 393-398. https://doi.org/10.1016/S0764-4442(00)88612-7
Z. Tan, F. Fang, On superlinear p(x)−Laplacian problems without Ambrosetti and Rabinowitz condition, Nonlinear Analysis 75 (2012) 3902-3915. https://doi.org/10.1016/j.na.2012.02.010
V. Zhikov, Averaging of functionals in the calculus of variations and elasticity, Math. USSR Izv. 29 (1987) 33-66. https://doi.org/10.1070/IM1987v029n01ABEH000958
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).